Solve $7x - 9 = 28 + 4(x - 1)$.
Answer (2)
Expand the right side of the equation: 7 x − 9 = 28 + 4 x − 4 .
Combine like terms: 7 x − 9 = 4 x + 24 .
Subtract 4 x from both sides: 3 x − 9 = 24 .
Add 9 to both sides: 3 x = 33 , then divide by 3 to find the solution: x = 11 .
Explanation
Understanding the Problem We are given the equation 7 x − 9 = 28 + 4 ( x − 1 ) and asked to solve for x . Our goal is to isolate x on one side of the equation.
Expanding the Equation First, we expand the right side of the equation by distributing the 4:
7 x − 9 = 28 + 4 x − 4
Combining Like Terms Next, we combine like terms on the right side of the equation:
7 x − 9 = 4 x + 24
Isolating x Terms Now, we subtract 4 x from both sides of the equation to get the x terms on the left side:
7 x − 4 x − 9 = 4 x − 4 x + 24
3 x − 9 = 24
Isolating the x Term We add 9 to both sides of the equation to isolate the x term:
3 x − 9 + 9 = 24 + 9
3 x = 33
Solving for x Finally, we divide both sides of the equation by 3 to solve for x :
3 3 x = 3 33
x = 11
Final Answer Therefore, the solution to the equation 7 x − 9 = 28 + 4 ( x − 1 ) is x = 11 .
Examples
Imagine you're trying to figure out how many hours you need to work this week to afford a new video game. You know your base expenses and how much you earn per hour. This problem is similar to solving for the number of hours (x) needed to balance your budget, where the equation represents your income and expenses. By solving for x, you determine the exact number of hours you need to work to achieve your financial goal. This type of algebraic problem is fundamental in personal finance and budgeting.
The solution to the equation 7 x − 9 = 28 + 4 ( x − 1 ) is found by expanding and simplifying both sides, leading to the final answer of x = 11 . This involves isolating x through a series of arithmetic operations. The key steps include distributing, combining like terms, and isolating the variable.
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